Questions tagged [topology]

A puzzle about disentangling knots, folding paper, separating strings and wires, and understanding the connectivity properties of elastic figures. General topology questions are off-topic but can be asked on Mathematics Stack Exchange.

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9
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2answers
821 views

How to generalise hang picture puzzle?

There is well known problem: The picture is attached to a string and you want to hang it on N nails so that if one takes out any of the nails, the picture falls. How do you do it? For those who ...
10
votes
2answers
2k views

The three utilities puzzle

Here is a variant of the three utilities puzzle. Famously, It is impossible to solve it on a plane paper (Euler's theorem can prove that). But can you solve it on a coffee mug? ...
7
votes
2answers
336 views

Teacup geometry

Inspired by the three utilities puzzle from prog_SAHIL I'm now posting a similar puzzle that makes use of the topology of a cup with a handle: The question is: How many distinct points can you ...
27
votes
5answers
9k views

Is there a proof that a map of the United States requires 4 colors?

The Four color theorem states that no more than four colors are required for any map. Can it be proved or disproved that 3 colors can be used for United States map?
3
votes
2answers
1k views

Are there any topology puzzles similar to The Seven Bridges of Königsberg?

Leonhard Euler proved that it is impossible to solve this puzzle: The challenge is to take a walk around the area depicted, and cross each bridge (yellow) exactly once. Using topology, Euler proved ...
30
votes
4answers
3k views

Smallest Unicode Box Drawing

What is the smallest box diagram you can draw which uses all of the Unicode box drawing characters at least once, but without leaving any loose ends? For reference, you must use each of these ...
8
votes
1answer
182 views

The grandest bridge in Appelhaken [duplicate]

In the capital of the grand country of Appelhaken there is a plane garden containing four magnificent monuments. So magnificent are they that the country has a Law requiring that there must be a ...
4
votes
2answers
849 views

Join six five-link chains to form a circular chain

Join six five-link chains to form a circular chain. To join two chains, you must cut, and then re-weld, a link. The final number of links in the circular chain will be 30. What is the minimum ...